Related papers: Two Koopman semigroups on discrete Lebesgue spaces

We study two classes of operator algebras associated with a unital subsemigroup $P$ of a discrete group $G$: one related to universal structures, and one related to co-universal structures. First we provide connections between universal…

In this paper we study continuous semigroups of positive operators on general vector lattices equipped with the relative uniform topology $\tau_{ru}$. We introduce the notions of strong continuity with respect to $\tau_{ru}$ and relative…

We consider second order uniformly elliptic operators of divergence form in $\R^{d+1}$ whose coefficients are independent of one variable. Under the Lipschitz condition on the coefficients we characterize the domain of the Poisson operators…

Given $1< p < q < \infty$ it is well know that the natural embedding of Lebesgue sequence spaces $\ell_p \hookrightarrow \ell_q$ is strictly singular. In this paper we extend this classical results and show that even the natural non-compact…

Given a bounded domain in the Euclidean space satisfying the uniform outer cone condition, we show that a uniformly elliptic operator of second order with continuous second order coefficients generates a holomorphic semigroup on the space…

In this paper, we consider topological semigroup actions on compact topological spaces. Under mild assumptions on the semigroup and the action, we construct a semi-direct product groupoid with a Haar system. We also show that it is…

We consider $\ell^r$ extensions of Calderon-Zygmund operators on weighted spaces $L^p(w)$ with $w$ an $A_p$ weight and $1 < p < \infty$. We give quantitative estimates of these operators' norm in terms of a given weight's $A_p$…

We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions $f$ in…

We construct nontrivial examples of weak-$C_p$ ($1\leq p \leq \infty$) operator spaces with the local operator space structure very close to $C_p = [R, C]_{\frac{1}{p}}$. These examples are non-homogeneous Hilbertian operator spaces, and…

We introduce new function spaces $\mathcal{L}_{W,s}^{q,p}(\mathbb{R}^{n})$ that yield a natural reformulation of the $\ell^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean…

Assuming the existence of the L-operators, we study the Hopf algebroid structure of U_{q,p}(B_N^{(1)}). As an application, we derive the type I and II vertex operators, which intertwine the U_{q,p}(B_N^{(1)})-modules of generic level, by…

We give an account of the theory of $E_0$-semigroups. We first focus on Arveson's contributions to the field and related results. Then we present the recent development of type II and type III $E_0$-semigroups. We also include a short note…

In this work we obtain sharp $L^p$-estimates for pseudo-differential operators on arbitrary graded Lie groups. The results are presented within the setting of the global symbolic calculus on graded Lie groups by using the Fourier analysis…

In this paper we introduce the notion of weighted (weakly) almost periodic compactifcation of a semitopological semigroup and generalize this notion to corresponding notion for transformation semigroup.The inclusion relation and equality of…

In this note, we establish $L^p$-bounds for the semigroup $e^{-tq^w(x,D)}$, $t \ge 0$, generated by a quadratic differential operator $q^w(x,D)$ on $\mathbb{R}^n$ that is the Weyl quantization of a complex-valued quadratic form $q$ defined…

We study the dynamics of the group of isometries of $L_p$-spaces. In particular, we study the canonical actions of these groups on the space of $\delta$-isometric embeddings of finite dimensional subspaces of $L_p(0,1)$ into itself, and we…

We prove the first theorem on projections on general noncommutative $\mathrm{L}^p$-spaces associated with non-type I von Neumann algebras where $1 \leqslant p < \infty$. This is the first progress on this topic since the seminal work of…

Very recently, \v{S}pakula and Tikuisis provide a new characterisation of (uniform) Roe algebras via quasi-locality when the underlying metric spaces have straight finite decomposition complexity. In this paper, we improve their method to…

In this paper we construct a compact quantum semigroup structure on the Toeplitz algebra $\mathcal{T}$. The existence of a subalgebra, isomorphic to the algebra of regular Borel's measures on a circle with convolution product, in the dual…

Let G be a group of type FP_n and let p>1. In this paper we show that the reduced l^p-homology of G is dual to the reduced l^q-cohomology for \frac{1}{p}+\frac{1}{q}=1. In our main theorem we show that for a group of type FP_n with a…